Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define rep(i,n) for ((i)=1;(i)<=(n);(i)++)
#define per(i,n) for ((i)=n;(i)>=(1);(i)--)
using namespace std;
int n,i,f,pos[200005],ans;
int main(){
	cin>>n;
	rep(i,n){
		int x;cin>>x;
		pos[x]=i; 
	}
	per(i,n-1){
		if(!ans){
			if(pos[i]>pos[i+1]){
				ans=1;
				f=i+1;
				continue;
			}
		}
		if(pos[f]<pos[i]&&pos[i]<pos[i+1]) continue;
		if(pos[i]<pos[i+1]&&pos[i+1]<pos[f]) continue;
		if(pos[i+1]<pos[f]&&pos[f]<pos[i]) continue;
		ans++;f=i+1;
	}
	cout<<ans<<endl;
	return 0;
}